Method for performing mm-based noma communication and device therefor

ABSTRACT

A method by which a terminal performs a multi-dimensional modulation (MM)-based non-orthogonal multiple access (NOMA) communication can comprise the steps of: receiving, from a base station, control information indicating a terminal specific codebook for a terminal in a predefined codebook set for an MM-based encoder; and receiving a downlink data channel from the base station on the basis of the indicated terminal specific codebook, or performing MM-based encoding on the basis of the indicated terminal specific codebook and then transmitting an uplink data channel.

TECHNICAL FIELD

The present disclosure relates to a wireless communication system, andmore particularly, to a method for performing multi-dimensionalmodulation (MM) based non-orthogonal multiple access (NOMA)communication and device therefor.

BACKGROUND ART

The next-generation 5G system has considered a wireless sensor network(WSN), massive machine type communication (MTC), etc. where a smallpacket is intermittently transmitted to achieve massive connection/lowcost/low power services.

In the case of a massive MTC service, connection density requirementsare strictly limited, but data rates and end-to-end (E2E) latencyrequirements are unrestricted (for example, connection density: up to200,000/km2, E2E latency: seconds to hours, and downlink/uplink (DL/UL)data rate: typically 1 to 100 kbps).

DISCLOSURE Technical Problem

An object of the present disclosure is to provide a method ofperforming, by a user equipment (UE), MM-based NOMA communication.

Another object of the present disclosure is to provide a method ofperforming, by a base station, MM-based NOMA communication.

Still another object of the present disclosure is to provide a UE forperforming MM-based NOMA communication.

A further object of the present disclosure is to provide a base stationfor performing MM-based NOMA communication.

It will be appreciated by persons skilled in the art that the objectsthat could be achieved with the present disclosure are not limited towhat has been particularly described hereinabove and the above and otherobjects that the present disclosure could achieve will be more clearlyunderstood from the following detailed description.

Technical Solution

In an aspect of the present disclosure, provided herein is a method ofperforming, by a UE, MM-based NOMA communication. The method mayinclude: receiving, from a base station, control information indicatinga UE-specific codebook for the UE in a codebook set predefined for anMM-based encoder; and receiving a downlink data channel from the basestation based on the indicated UE-specific codebook or transmitting anuplink data channel after performing MM-based encoding based on theindicated UE-specific codebook. The predefined codebook set may beconfigured such that interference from multiple UEs caused bysuperposition access of the multiple UEs is minimized. The predefinedcodebook set may be configured such that when the base station performsdecoding, complexity of a message passing algorithm (MPA) is minimized.The indicated UE-specific codebook may be configured such that aEuclidean distance between complex column vectors in the indicatedUE-specific codebook is maximized. The control information may bereceived through a downlink control channel, radio resource control(RRC) signaling, or periodic control signaling. The control informationmay further include information on a modulation and coding scheme (MCS)index.

In another aspect of the present disclosure, provided herein is a methodof performing, by a base station, MM-based NOMA communication. Themethod may include: selecting a UE-specific codebook for a UE from acodebook set predefined for an MM-based encoder and performing MM-basedencoding of channel-coded bits based on the selected UE-specificcodebook; and transmitting, to the UE, control information includinginformation indicating the selected UE-specific codebook, wherein theMM-based encoding is applied to the control information; andtransmitting, to the UE, a downlink data channel based on the indicatedUE-specific codebook or receiving, from the UE, an uplink data channelto which the MM-based encoding is applied based on the indicatedUE-specific codebook.

In still another aspect of the present disclosure, provided herein is aUE for performing MM-based NOMA communication. The UE may include areceiver, a transmitter, and a processor. The processor may beconfigured to: control the receiver to receive, from a base station,control information indicating a UE-specific codebook for the UE in acodebook set predefined for an MM-based encoder; and control thereceiver to receive a downlink data channel from the base station basedon the indicated UE-specific codebook or control the transmitter totransmit an uplink data channel after performing MM-based encoding basedon the indicated UE-specific codebook. The predefined codebook set maybe configured such that interference from multiple UEs caused bysuperposition access of the multiple UEs is minimized. The predefinedcodebook set may be configured such that when the base station performsdecoding, complexity of an MPA is minimized. The indicated UE-specificcodebook may be configured such that a Euclidean distance betweencomplex column vectors in the indicated UE-specific codebook ismaximized. The control information may be received through a downlinkcontrol channel, RRC signaling, or periodic control signaling. Thecontrol information may further include information on an MCS index.

In a further aspect of the present disclosure, provided is a basestation for performing MM-based NOMA communication. The base station mayinclude: a processor configured to select a UE-specific codebook for aUE from a codebook set predefined for an MM-based encoder and performMM-based encoding of channel-coded bits based on the selectedUE-specific codebook; a transmitter configured to transmit, to the UE,control information including information indicating the selectedUE-specific codebook, wherein the MM-based encoding is applied to thecontrol information; and a receiver configured to transmit, to the UE, adownlink data channel based on the indicated UE-specific codebook orreceive, from the UE, an uplink data channel to which the MM-basedencoding is applied based on the indicated UE-specific codebook.

Advantageous Effects

According to the present disclosure, when a UE-specific codebook isused, a receiving end can reduce not only the complexity of decoding butinterference caused by multiuser superposition transmission so thatcommunication performance can be remarkably improved.

The effects that can be achieved through the embodiments of the presentdisclosure are not limited to what has been particularly describedhereinabove and other effects which are not described herein can bederived by those skilled in the art from the following detaileddescription.

DESCRIPTION OF DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the disclosure and are incorporated in and constitute apart of this specification, illustrate embodiments of the disclosure.

FIG. 1 is a block diagram for configurations of a base station 105 and auser equipment 110 in a wireless communication system 100.

FIG. 2 is a block diagram illustrating NOMA-based downlinktransmission/reception (Tx/Rx) between communication devices.

FIG. 3 is a block diagram illustrating NOMA-based uplink Tx/Rx betweencommunication devices.

FIG. 4 is a block diagram illustrating downlink Tx/Rx betweencommunication devices based on NOMA and non-orthogonal spreading codes,and FIG. 5 is a block diagram illustrating uplink Tx/Rx betweencommunication devices based on NOMA and non-orthogonal spreading codes.

FIG. 6 is a diagram for explaining an MM-based NOMA operation.

FIG. 7 is a diagram illustrating a case in which there are three or fourvectors in a 2-dimensional (2D) plane.

FIG. 8 is a diagram illustrating a single base constellation.

FIG. 9 is a diagram illustrating mother constellations according to FIG.8.

FIG. 10 is a diagram illustrating superposition of constellations.

FIG. 11 is a diagram illustrating two base constellations

FIG. 12 is a diagram illustrating mother constellations according toFIG. 11.

FIG. 13 is a diagram illustrating superposition of constellations

FIG. 14 is a diagram illustrating a single asymmetric base constellation

FIG. 15 is a diagram illustrating mother constellations according toFIG. 14.

FIG. 16 is a diagram illustrating an asymmetric 2D base constellation

FIG. 17 is a diagram illustrating mother constellations according toFIG. 16.

FIG. 18 is a diagram illustrating the performance of an MPA decoderaccording to Embodiments 1, 2, 3, and 4.

FIG. 19 is a diagram illustrating a method of exchanging and signalinginformation on a codebook for MM-based NOMA in downlink scheduling basedtransmission, and FIG. 20 is a diagram illustrating a method ofexchanging and signaling information on a codebook for MM-based NOMA inuplink scheduling based transmission.

FIG. 21 is a diagram illustrating a method of exchanging and signalinginformation on a codebook for MM-based NOMA in downlink scheduling basedtransmission, and FIG. 22 is a diagram illustrating a method ofexchanging and signaling information on a codebook for MM-based NOMA inuplink scheduling based transmission.

FIGS. 23 and 24 are diagrams illustrating contention-based transmissionin an MM-based NOMA system. Specifically, FIG. 23 illustrates signalflow in a contention-based transmission system based on UE-specificcodebook allocation, and FIG. 24 illustrates signal flow in acontention-based transmission system based on UE-specific codebookselection.

BEST MODE

Reference will now be made in detail to the preferred embodiments of thepresent disclosure, examples of which are illustrated in theaccompanying drawings. In the following detailed description of thedisclosure includes details to help the full understanding of thepresent disclosure. Yet, it is apparent to those skilled in the art thatthe present disclosure can be implemented without these details. Forinstance, although the following descriptions are made in detail on theassumption that a mobile communication system includes 3GPP LTE system,the following descriptions are applicable to other random mobilecommunication systems in a manner of excluding unique features of the3GPP LTE.

Occasionally, to prevent the present disclosure from getting vaguer,structures and/or devices known to the public are skipped or can berepresented as block diagrams centering on the core functions of thestructures and/or devices. Wherever possible, the same reference numberswill be used throughout the drawings to refer to the same or like parts.

Besides, in the following description, assume that a terminal is acommon name of such a mobile or fixed user stage device as a userequipment (UE), a mobile station (MS), an advanced mobile station (AMS)and the like. And, assume that a base station (BS) is a common name ofsuch a random node of a network stage communicating with a terminal as aNode B (NB), an eNode B (eNB), an access point (AP) and the like.Although the present specification is described based on IEEE 802.16msystem, contents of the present disclosure may be applicable to variouskinds of other communication systems.

In a mobile communication system, a user equipment is able to receiveinformation in downlink and is able to transmit information in uplink aswell. Information transmitted or received by the user equipment node mayinclude various kinds of data and control information. In accordancewith types and usages of the information transmitted or received by theuser equipment, various physical channels may exist.

Moreover, in the following description, specific terminologies areprovided to help the understanding of the present disclosure. And, theuse of the specific terminology can be modified into another form withinthe scope of the technical idea of the present disclosure.

FIG. 1 is a block diagram illustrating the configurations of a basestation 105 and a user equipment 110 in a wireless communication system100.

Although one base station 105 and one user equipment 110 (D2D userequipment included) are shown in the drawing to schematically representa wireless communication system 100, the wireless communication system100 may include at least one base station and/or at least one userequipment.

Referring to FIG. 1, a base station 105 may include a transmitted (Tx)data processor 115, a symbol modulator 120, a transmitter 125, atransceiving antenna 130, a processor 180, a memory 185, a receiver 190,a symbol demodulator 195 and a received data processor 197. And, a userequipment 110 may include a transmitted (Tx) data processor 165, asymbol modulator 170, a transmitter 175, a transceiving antenna 135, aprocessor 155, a memory 160, a receiver 140, a symbol demodulator 155and a received data processor 150. Although the base station/userequipment 105/110 includes one antenna 130/135 in the drawing, each ofthe base station 105 and the user equipment 110 includes a plurality ofantennas. Therefore, each of the base station 105 and the user equipment110 of the present disclosure supports an MIMO (multiple input multipleoutput) system. And, the base station 105 according to the presentdisclosure may support both SU-MIMO (single user-MIMO) and MU-MIMO(multi user-MIMO) systems.

In downlink, the transmitted data processor 115 receives traffic data,codes the received traffic data by formatting the received traffic data,interleaves the coded traffic data, modulates (or symbol maps) theinterleaved data, and then provides modulated symbols (data symbols).The symbol modulator 120 provides a stream of symbols by receiving andprocessing the data symbols and pilot symbols.

The symbol modulator 120 multiplexes the data and pilot symbols togetherand then transmits the multiplexed symbols to the transmitter 125. Indoing so, each of the transmitted symbols may include the data symbol,the pilot symbol or a signal value of zero. In each symbol duration,pilot symbols may be contiguously transmitted. In doing so, the pilotsymbols may include symbols of frequency division multiplexing (FDM),orthogonal frequency division multiplexing (OFDM), or code divisionmultiplexing (CDM).

The transmitter 125 receives the stream of the symbols, converts thereceived stream to at least one or more analog signals, additionallyadjusts the analog signals (e.g., amplification, filtering, frequencyupconverting), and then generates a downlink signal suitable for atransmission on a radio channel. Subsequently, the downlink signal istransmitted to the user equipment via the antenna 130.

In the configuration of the user equipment 110, the receiving antenna135 receives the downlink signal from the base station and then providesthe received signal to the receiver 140. The receiver 140 adjusts thereceived signal (e.g., filtering, amplification and frequencydownconverting), digitizes the adjusted signal, and then obtainssamples. The symbol demodulator 145 demodulates the received pilotsymbols and then provides them to the processor 155 for channelestimation.

The symbol demodulator 145 receives a frequency response estimated valuefor downlink from the processor 155, performs data demodulation on thereceived data symbols, obtains data symbol estimated values (i.e.,estimated values of the transmitted data symbols), and then provides thedata symbols estimated values to the received (Rx) data processor 150.The received data processor 150 reconstructs the transmitted trafficdata by performing demodulation (i.e., symbol demapping, deinterleavingand decoding) on the data symbol estimated values.

The processing by the symbol demodulator 145 and the processing by thereceived data processor 150 are complementary to the processing by thesymbol modulator 120 and the processing by the transmitted dataprocessor 115 in the base station 105, respectively.

In the user equipment 110 in uplink, the transmitted data processor 165processes the traffic data and then provides data symbols. The symbolmodulator 170 receives the data symbols, multiplexes the received datasymbols, performs modulation on the multiplexed symbols, and thenprovides a stream of the symbols to the transmitter 175. The transmitter175 receives the stream of the symbols, processes the received stream,and generates an uplink signal. This uplink signal is then transmittedto the base station 105 via the antenna 135. In the base station 105,the uplink signal is received from the user equipment 110 via theantenna 130. The receiver 190 processes the received uplink signal andthen obtains samples. Subsequently, the symbol demodulator 195 processesthe samples and then provides pilot symbols received in uplink and adata symbol estimated value. The received data processor 197 processesthe data symbol estimated value and then reconstructs the traffic datatransmitted from the user equipment 110.

The processor 155/180 of the user equipment/base station 110/105 directsoperations (e.g., control, adjustment, management, etc.) of the userequipment/base station 110/105. The processor 155/180 may be connectedto the memory unit 160/185 configured to store program codes and data.The memory 160/185 is connected to the processor 155/180 to storeoperating systems, applications and general files. The processor 155/180may be called one of a controller, a microcontroller, a microprocessor,a microcomputer and the like. And, the processor 155/180 may beimplemented using hardware, firmware, software and/or any combinationsthereof. In the implementation by hardware, the processor 155/180 may beprovided with such a device configured to implement the presentdisclosure as ASICs (application specific integrated circuits), DSPs(digital signal processors), DSPDs (digital signal processing devices),PLDs (programmable logic devices), FPGAs (field programmable gatearrays), and the like. Meanwhile, in case of implementing theembodiments of the present disclosure using firmware or software, thefirmware or software may be configured to include modules, procedures,and/or functions for performing the above-explained functions oroperations of the present disclosure. And, the firmware or softwareconfigured to implement the present disclosure is loaded in theprocessor 155/180 or saved in the memory 160/185 to be driven by theprocessor 155/180.

Layers of a radio protocol between a user equipment/base station and awireless communication system (network) may be classified into 1st layerL1, 2nd layer L2 and 3rd layer L3 based on 3 lower layers of OSI (opensystem interconnection) model well known to communication systems. Aphysical layer belongs to the 1st layer and provides an informationtransfer service via a physical channel. RRC (radio resource control)layer belongs to the 3rd layer and provides control radio resourcedbetween UE and network. A user equipment and a base station may be ableto exchange RRC messages with each other through a wirelesscommunication network and RRC layers.

In the present specification, although the processor 155/180 of the userequipment/base station performs an operation of processing signals anddata except a function for the user equipment/base station 110/105 toreceive or transmit a signal, for clarity, the processors 155 and 180will not be mentioned in the following description specifically. In thefollowing description, the processor 155/180 can be regarded asperforming a series of operations such as a data processing and the likeexcept a function of receiving or transmitting a signal without beingspecially mentioned.

The present disclosure proposes transmission methods for multiusersuperposition access based on non-orthogonal and orthogonal codebooks.

FIG. 2 is a block diagram illustrating NoMA-based downlinktransmission/reception (Tx/Rx) between communication devices.

The Tx/Rx structure for downlink support shown in FIG. 2 is generallyused in a NOMA system where multiuser information is allocated to thesame resource and transmitted thereon. In the 3GPP standardization, theNoMA system is referred to as ‘multiuser superposition transmission(MUST) system’. Since information for multiple UEs is superposed andtransmitted on the same time-frequency resource in the NOMA system, itcan guarantee high transmission capacity and increase the number ofsimultaneous accesses compared to the legacy LTE system. Thus, the NoMAsystem is considered as a core technology for the next-generation 5Gsystem. For example, the NOMA-based technology for the next-generation5G system may include: MUST where UEs are identified based on theirpower levels; sparse code multiple access (SCMA) where modulation isperformed based on a sparse complex codebook; and interleave divisionmultiple access (IDMA) where a UE-specific interleaver is used.

Referring to FIG. 2, in the MUST system, a transmitting end modulatesdata for multiple UEs and then allocates different power to each symbol.Alternatively, the transmitting end hierarchically modulates the datafor multiple UEs based on hierarchical modulation and then transmits thehierarchically modulated data. A receiving end demodulates the data formultiple UEs (hereinafter such data is referred to as multi-UE data)based on multiuser detection (MUD). In the SCMA system, the transmittingend transmits multi-UE data by replacing a forward error correction(FEC) encoder and a modulation procedure for the multi-UE data with apredetermined sparse complex codebook modulation scheme. The receivingend demodulates the multi-UE data based on the MUD.

In the IDMA system, the transmitting end modulates and transmits FECencoding information for multi-UE data using UE-specific interleavers,and the receiving end demodulates the multi-UE data based on the MUD.

Each of the systems may demodulate multi-UE data using various MUDschemes. For example, the MUD schemes may include maximum likelihood(ML), maximum joint a posteriori probability (MAP), message passingalgorithm (MPA), matched filtering (MF), successive interferencecancellation (SIC), parallel interference cancellation (PIC), codewordinterference cancellation (CWIC), etc. In this case, the demodulationcomplexity and processing time delay may vary depending on modulationschemes or the number of demodulation attempts.

FIG. 3 is a block diagram illustrating NoMA-based uplink Tx/Rx betweencommunication devices.

Specifically, FIG. 3 shows the Tx/Rx structure for uplink support in aNoMA-based system where information for multiple UEs (hereinafter suchinformation is referred to as multi-UE information) is allocated to thesame resource and transmitted thereon. In each of the systems, atransmitting end may transmit multi-UE data in the same manner asdescribed in FIG. 2, and a receiving end may demodulate the multi-UEdata in the same manner as described in FIG. 2. Since the NoMA-basedsystem superposes and transmits signals for multiple UEs on the sametime-frequency resource, it has a high decoding error rate compared tothe LTE system but may support high frequency usage efficiency or largeconnectivity. In other words, the NoMA system may guarantee highfrequency usage efficiency or large connectivity with no increase in thedecoding error rate by controlling the coding rate according to systemenvironments.

There is inevitable interference between multi-UE data in the NOMA-basedsystem since the multi-UE data is allocated to the same resource,compared to a case where data is allocated for a single UE. A signal ata kth receiving end in the NOMA-based system in FIG. 2 may be simplyexpressed as shown in Equation 1.

y _(k)=Σ_(n=1) ^(K) h _(k) s _(n) +n _(k) =h _(k) s _(k)+Σ_(n≠k,n=1)^(K) h _(k) s _(n) +n _(k)  [Equation 1]

In Equation 1, h_(k) means a channel from the transmitting end to thekth receiving end, s_(k) means a data symbol to the kth receiving end,and n_(k) means signal noise. K is the number of multiple UEs allocatedto the same time-frequency resource. The second term (Σ_(n≠k,n=1)^(K)h_(k)s_(n)) of the third formula of Equation 1 indicates a MultiuserInterference (MUI) signal caused by data symbols to other receivingends. Therefore, the transmission capacity according to the receivedsignal may be simply expressed as shown in Equation 2 below.

$\begin{matrix}{\mspace{79mu} {{{{C = {\sum_{k = 1}^{K}R_{k}}}R_{k}} = {{\log_{2}\left( {1 + \frac{{{h_{k}s_{k}}}^{2}}{\begin{matrix}{{{\sum_{{n \neq k},{n = 1}}^{K}{h_{k}s_{n}}}}^{2} +} \\\sigma_{k}\end{matrix}}} \right)} = {\log_{2}\left( {1 + \frac{{Channel}\mspace{14mu} {Gain}}{{MUI} + {Noise}}} \right)}}},\mspace{79mu} {\forall k}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

Regarding the transmission capacity in Equation 2, since the number ofadded R_(k) values increases as K increases, it is expected that C alsoincreases. However, considering that MUI increases as K increases, eachof the R_(k) values decreases so that the entire transmission capacity Cmay decrease. Even if a MUD scheme may demodulate data for each UE whileeffectively decreasing the MUI, the presence of the MUI decreases theentire transmission capacity and requires high-complexity MUD. If theMUI caused by the multi-UE data transmission is minimized, thetransmission capacity is expected to be higher. Alternatively, if theMUI caused by the multi-UE data transmission is able to be controlledquantitatively, the transmission capacity may be improved by schedulingsuperposition between the multi-UE data.

FIG. 4 is a block diagram illustrating downlink Tx/Rx betweencommunication devices based on NOMA and non-orthogonal spreading codes,and FIG. 5 is a block diagram illustrating uplink Tx/Rx betweencommunication devices based on NOMA and non-orthogonal spreading codes.

Among NOMA techniques, a non-orthogonal codebook based technique (e.g.,SCMA, CDMA, etc.) assumes a multiple access scheme using non-orthogonalspreading codes when multiuser data is superposed and transmitted on thesame time-frequency resource through spreading. Specifically, FIG. 4shows the structures of transmitting and receiving ends for downlinktransmission in a NOMA system where multiuser data is superposed andtransmitted using UE-specific spreading codes when the multiuser data isallocated to the same time-frequency resource, and FIG. 5 shows thestructures of transmitting and receiving ends for uplink transmission inthe same NOMA system. Although FIGS. 4 and 5 show that the UE-specificspreading codes are used in the frequency domain, the UE-specificspreading codes may also be used in the time domain.

Using a predefined codebook, each of transmitting and receiving endsallocates a UE-specific spreading code to each user. In this case, theUE-specific spreading code may be expressed as shown in Equation 3.

$\begin{matrix}{C = {\begin{bmatrix}c^{(1)} & \ldots & c^{(K)}\end{bmatrix} = \begin{bmatrix}c_{1}^{(1)} & \ldots & c_{1}^{(K)} \\\vdots & \ddots & \vdots \\c_{N}^{(1)} & \ldots & c_{N}^{(K)}\end{bmatrix}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

A UE-specific spreading codebook is a codebook satisfying the conditionof C⊂

^(N×K) and has the characteristics shown in Equation 4.

Using a predefined codebook, each of transmitting and receiving endsallocates a UE-specific spreading code to each user. In this case, theUE-specific spreading code may be expressed as shown in Equation 4.

$\quad\begin{matrix}\left\{ \begin{matrix}{{{{c^{{(k)}*} \cdot c^{(k)}}} = 1},{\forall k},{k = 1},\ldots \mspace{14mu},K,} \\{{{{c^{{(k)}*} \cdot c^{(j)}}} = \delta_{kj}},{\forall k},{\forall j},{k \neq j},{k = 1},\ldots \mspace{14mu},K,{j = 1},\ldots \mspace{14mu},K,}\end{matrix} \right. & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

In addition, a NOMA technique capable of spreading an encoded bit streaminto complex symbol vectors based on modulation and a non-orthogonalcodebook may be considered. This technique corresponds to amulti-dimensional modulation (MM) based NoMA technique, where sparsitymay exist or not.

FIG. 6 is a diagram for explaining an MM-based NOMA operation.

In the example of FIG. 6, a kth UE (UE k) creates an information bitstream for generated traffic and converts the created information bitstream into an encoded bit stream by performing channel coding thereon.The MM-based encoder of the kth UE (UE k) converts encoded bits into acomplex vector based on a UE-specific codebook k. FIG. 6 shows thatencoded two bits are converted into a complex vector consisting of fourcomplex symbols. For example, if encoded bits are [0 0], the encodedbits are converted into a complex vector, [c_(1,1), c_(1,1), c_(3,1),c_(4,1)]^(T). To transmit the converted complex vector, resource mappingand inverse fast Fourier transform (IFFT) are applied. The operationshown in FIG. 6 is applied to downlink transmission in a similar manner,and in this case, a receiving end decodes encoded bits using a messagepassing algorithm (MPA).

In the operation of FIG. 6, a UE-specific codebook may be applied to amultiuser superposition access scheme based on the characteristics ofthe codebook. However, when decoding is performed based on the MPA, thecoefficients of converted complex vectors of other users may act asinterference. Thus, a codebook design capable of minimizing interferencefrom other users is required. The following terms are used herein toexplain a relevant process.

J: Cardinality of Codewords (or Expected connected UEs)=The number ofFunction Nodes (the number of multiple users)

K: Dimension of Codeword (or the number of resources)=The number ofVariable Nodes

M: Order of Multi-dimensional Modulation (for log 2(M) bitstransmission)

d_(v): Sparsity of Codeword (or the number of Non-zero coefficients)

d_(f): The number of Superposed coefficients (or the number of UEsconnected to the same resource)

OF: Overloading Factor=J/K

In an MM-based NOMA scheme among the NOMA techniques, the design of anMM-based encoder determines the decoding performance of a receiver (orreceiving end). However, in the case of the MM-based encoder, there isonly an exemplary codebook created by computer simulation, and there isno codebook design rule for designing the MM-based encoder or nocodebook optimized therefor. Accordingly, the present disclosureproposes a codebook design method and codebook for optimizing theperformance of the MM-based encoder. Further, the present disclosureproposes a method of designing entire codebook sets for UE-specificcodebooks for the MM-based encoder in MM-based NOMA communication, anoptimized codebook set, and a method of exchanging and signalinginformation on a codebook.

Embodiment 1: Codebook Design for MM-Based Encoder

The MM-based NOMA codebook should be designed as follows.

(Rule 1) Design of Bipartite Matching Rule for MPA Complexity Reduction

Each coefficient of a UE-specific codebook affects the amount ofcomputation for MPA operation. As the number of zero coefficientsincreases, the complexity of the MAP operation may decrease.

(Rule 1-1) Complete bipartite matching is defined as follows.

$F_{c} = {\begin{matrix}{VN}_{1} \\\vdots \\{vN}_{K}\end{matrix}\begin{matrix}\begin{matrix}{FN}_{1} & \ldots & {FN}_{J}\end{matrix} \\\begin{bmatrix}1 & \ldots & 1 \\\vdots & \ddots & \vdots \\1 & \ldots & 1\end{bmatrix}\end{matrix}}$

In this case, d_(v)=K and d_(f)=J. Considering that the complexity of anMPA is affected by d_(v) and d_(f), it is necessary to guaranteedecoding performance while reducing d_(v) (the number of non-zerocoefficients) and d_(f) (the number of UEs connected or allocated to thesame resource).

For example, when multiuser superposition access is supported for sixusers (J=6) through four complex coefficients (K=4), a factor graph maybe defined as

${F\left( {{K = 4},{J = 6}} \right)} = \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 0\end{bmatrix}$

to reduce the complexity of the MPA. Since d_(v)=2 and d_(f)=3 in theabove definition, it is expected that the complexity is reduced comparedto complete bipartite matching.

(Rule 1-2) UE 1 creates a UE-specific codebook using the vectorcorresponding to the first column of the factor graph,

${F\left( {{K = 4},{J = 6}} \right)} = {\begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 0\end{bmatrix}.}$

For example, UE-specific codebook 1 is configured by

${F\left( {{UE} = 1} \right)} = {\begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}.}$

When M (modulation order)=4, the codebook for the MM-based encoder maybe designed as follow: UE specific

$\; {1 = {\begin{matrix}\begin{matrix}00 & {\; 01} & 11 & {\mspace{11mu} 10}\end{matrix} \\\begin{bmatrix}0 & 0 & 0 & 0 \\c_{2,1} & c_{2,2} & c_{2,3} & c_{2,4} \\0 & 0 & 0 & 0 \\c_{4,1} & c_{4,2} & c_{4,3} & c_{4,4}\end{bmatrix}\end{matrix}.}}$

In this case, for example, bits ‘00’, ‘01’, ‘10’, and ‘10’ may indicatethe vector corresponding to the first column, the vector correspondingto the second column, the vector corresponding to the third column, andthe vector corresponding to the fourth column, respectively.

(Rule 1-3) The MM-based encoder needs to determine a mappingrelationship between encoded bits and a complex vector with respect to adistance between complex column vectors in the UE-specific codebookaccording to the Gray mapping rule. Considering channel coding, theEuclidean distance in the bit domain and the Euclidean distance betweencomplex symbol vectors should be calculated in the same manner to obtaingood decoding performance. For example, when the Euclidean distancebetween column vectors 1 and 4 of the UE-specific codebook is greatest,column vectors 1 and 4 correspond to encoded bits [0 0] and encoded bits[1 1], respectively, and thus, the Euclidean distance in the bit domainmay be maximized as well. Similarly, when the Euclidean distance betweencolumn vectors 2 and 3 of the UE-specific codebook is greatest, columnvectors 2 and 3 correspond to encoded bits [0 1] and encoded bits [1 0],respectively, and thus, the Euclidean distance in the bit domain may bemaximized as well.

(Rule 2) Design of Base Constellation for Improving UE-specific CodebookDecoding Performance of Each User (or UE)

When decoding is performed based on the MPA, detection needs to beperformed using a complex vector to decode transmitted encoded bits.Thus, the Euclidean distance between complex vectors in the UE-specificcodebook of each user should be maximized FIG. 7 illustrates a case inwhich there are three or four vectors in a 2-dimensional (2D) plane.

For example, the condition of max min distance (c_(i),c_(j)), where i,≠j, i,j=1 . . . 4 needs to be satisfied to maximize the Euclideandistance of UE-specific codebook 1 ([c₁ c₂ c₃ c₄]) described in Rule 1.In other words, when vector 1 is orthogonal to vector 2 in a 2D planeand when the phase of vector 1 is opposite to that of vector 4 and thephase of vector 2 is opposite to that of vector 3, the Euclideandistance may be maximized. For example, when UE-specific codebook 1 is

$\begin{bmatrix}1 & 1 & {- 1} & {- 1} \\{- 1} & 1 & {- 1} & 1\end{bmatrix},$

the phases of vectors 1 and 2 are opposite to those of vectors 4 and 3,respectively while vector 1 is orthogonal to vector 2. A number ofvector sets satisfy this condition and may be combined with other designrules.

(Rule 3) Design of Mother Constellation for Interference Control betweenMultiple Users

Multiple users transmit different complex coefficients according toUE-specific codebooks. As a result, there are (d_(f)−1) pieces ofinterference due to bipartite matching. The Euclidean distance betweencomplex coefficients needs to be maximized to minimize interference andimprove the decoding performance of an MPA. For example, considering thefactor graph for the bipartite matching described in Rule 1,

${{F\left( {{K = 4},{J = 6}} \right)} = \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 0\end{bmatrix}},$

UE 1 creates its UE-specific codebook using the vector corresponding tothe first column of the matrix. That is, when the UE-specific codebookis created by

${{F\left( {{UE} = 1} \right)} = \begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}},$

there is interference from another user having a complex coefficient inthe second row. This interference may be expressed as shown in Table 1.

Therefore, a constellation design for maximizing the Euclidean distancebetween complex coefficients of each UE-specific codebook of multiuseris required. For example, when d_(f)=3 and M=4, three UEs transmit aplurality of coefficients on one resource. In this case, since fourconstellations are configured for each UE according to the value of M,there may be a total of 12 complex coefficients. Assuming thatconstellations used by UE 1, UE 2, and UE 3 are [a(1), a(2), a(3),a(4)], [b(1), b(2), b(3), b(4)], and [c(1), c(2), c(3), c(4)],respectively, complex symbols superposed on one resource may berepresented as follows: superposition of constellations (i, j,k)=a(i)+b(j)+c(k), where i, j, k=1, . . . , M. Accordingly, thesuperposition of constellations (i, j, k) may be represented by a totalof M^(d) ^(f) (4³=64) combinations. To minimize multiuser interference(or decode a superposed signal), a constellation design for maximizingthe Euclidean distance between superposed constellations is required.

(Rule 4) Design of Mother Constellation in Consideration ofContention-based Transmission

In Rule 3, superposition transmission is performed according toscheduling so that interference from all users (or UEs) is optimized.However, in the case of contention-based transmission, all users may notperform transmission. In this case, since multiple symbols may not besuperposed and transmitted on one resource, the optimization ofEuclidean distances in a constellation represented on one resource mayaffect decoding performance. Therefore, a constellation design needs toconsider the optimization of Euclidean distances in the constellationrepresented on one resource. That is, for the bipartite matchingdetermined in Rule 1, Euclidean distances between all motherconstellations used for optimizing Rule 2 are maximized

(Rule 5) Design of Bipartite Matching Rule Extension for Providing HighConnectivity

The codebook design of Rule 1 that satisfies Rules 2, 3, and 4 is anNP-hard problem due to non-convex optimization. As a result, it is verydifficult to design a codebook as the values of J and K increase. Tosimplify the codebook design, bipartite matching rule extension isproposed.

It is assumed that in Rule 1, the minimum unit of the bipartitematching, F(K=4, J=6) is designed according to Rule 3. Using theCartesian product of an identity matrix and F(K=4J=6), a bipartitematching pattern may be extended as follows:

${F\left( {{K = 8},{J = 12}} \right)} = {{F\left( {{K = {4*2}},{J = {6*2}}} \right)} = {{I_{2 \times 2} \times {F\left( {{K = 4},{J = 6}} \right)}} = {\begin{bmatrix}{F\left( {{K = 4},{J = 6}} \right)} & 0 \\0 & {F\left( {{K = 4},{J = 6}} \right)}\end{bmatrix}.}}}$

The above equation may be generalized as follows:

${F\left( {{m\; K},{m\; J}} \right)} = {{I_{m \times m} \times {F\left( {K,J} \right)}} = {\begin{bmatrix}{F\left( {K,J} \right)} & \ldots & 0 \\\vdots & \ddots & \vdots \\0 & \ldots & {F\left( {K,J} \right)}\end{bmatrix}.}}$

The above-described codebook design is an NP-hard problem due tonon-convex optimization. As a result, it is very difficult to design anoptimized codebook that satisfies all conditions. Accordingly, thepresent disclosure describes a method of increasing the decoding rate ofa multiuser superposition signal through the MPA of a receiving end byrelaxing some of the rules with reference to the following embodiments.

Embodiment 1: Optimization of Rules 1 and 2 and Relaxation of Rule 3(Single Base Constellation Based Codebook Design)

In Embodiment 1, Rule 1 is optimized for the case where

${{F\left( {{K = 4},{J = 6}} \right)} = \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 0\end{bmatrix}},$

d_(v)=2, and d_(f)=3. In the case, if this factor graph is changed by alinear combination of each column vector or row vector thereof, itscharacteristics are not changed. To optimize Rule 2, the following baseconstellation and phase rotation are proposed.

FIG. 8 illustrates a single base constellation.

In FIG. 8, base constellation: B=[B1, B2, B3, B4], where B1=−3, B2=−1,B3=1, and B4=3 and

${{{Phase}\mspace{14mu} {Rotation}\text{:}\mspace{14mu} \theta_{i}} = {\frac{i - 1}{d_{f}}*\pi}},{{{where}\mspace{14mu} i} = 1},{\ldots \mspace{14mu} {d_{f}.}}$

Then, mother constellations may be configured by the base constellationand phase rotation as follows.

FIG. 9 illustrates mother constellations according to FIG. 8.

The mother constellations of FIG. 9 may be expressed as follows:

Mother Constellation 1: a=B*exp(j*θ ₁)=B=[a(1),a(2),a(3)a(4)]

Mother Constellation 2: b=B*exp(j*θ ₂)=B*exp(j*⅓π=[b(1),b(2),b(3),b(4)]

Mother Constellation 3: c=B*exp(j*θ ₃)=B*exp(j*⅔π=[c(1),c(2),c(3),c(4)].

For the optimization of Rule 2, the constellations may be mapped to theUE-specific codebook of each user as follows.

${{{Since}\mspace{20mu} {F\left( {{UE} = 1} \right)}} = \begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 2} \right)}} = \begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 2} = \begin{bmatrix}a \\0 \\{P*c^{T}} \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 3} \right)}} = \begin{bmatrix}1 \\1 \\0 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 3} = \begin{bmatrix}{P*b^{T}} \\a \\0 \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 4} \right)}} = \begin{bmatrix}0 \\0 \\1 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 4} = \begin{bmatrix}0 \\0 \\b \\{P*c^{T}}\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 5} \right)}} = \begin{bmatrix}1 \\0 \\0 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 5} = \begin{bmatrix}{P*c^{T}} \\0 \\0 \\b\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 6} \right)}} = \begin{bmatrix}0 \\1 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 6} = \begin{bmatrix}0 \\{P*b^{T}} \\a \\0\end{bmatrix}},{where}$ $P = {\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.}$

To improve the UE-specific codebook decoding performance of each user,the permutation matrix, P maximizes the Euclidean distance betweencomplex vectors in the UE-specific codebook of each user according toRule 2. For example, assuming that column vectors

${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {\begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix} = \begin{bmatrix}0 & 0 & 0 & 0 \\{c(2)} & {c(4)} & {c(1)} & {c(3)} \\0 & 0 & 0 & 0 \\{a(1)} & {a(2)} & {a(3)} & {a(4)}\end{bmatrix}}$

of are vector 1, 2, 3, and 4, respectively, the phases of vectors 1 and2 are opposite to those of vectors 4 and 3, respectively sincec(1)=−c(4), c(2)=−c(3), a(1)=−a(4), and a(2)=−a(3). In addition, sinceconjugate(c(2))*c(4)+conjugate(a(1))*a(2)=0, vector 1 is orthogonal tovector 2. Since the vector relationship is equally applied to allUE-specific codebooks, Rule 2 is optimized. By substituting theUE-specific codebooks into the factor graph for the bipartite matchingobtained from Rule 1, Equation 5 is obtained.

$\begin{matrix}{{F\left( {{K = 4},{J = 6}} \right)} = \left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

Meanwhile, in Rule 3, the superposition of constellations (i, j, k) mayhave a total of M^(d) ^(f) (4³=64) combinations as shown in FIG. 10.

FIG. 10 illustrates superposition of constellations.

In FIG. 10, the x axis corresponds to the real domain of theconstellation superposition, and the y axis corresponds to the imaginarydomain of the constellation superposition. In FIG. 10, it can be seenfrom superposition of constellation patterns that some constellationsare superposed. That is, Rule 3 may not be optimized depending oncombination of traffic of each user. The entire codebook may beexpressed as shown in Equation 6.

$\begin{matrix}{{{{F\left( {{K = 4},{J = 6}} \right)} = \left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack}\mspace{20mu} {{{a = \left\lbrack {{- 3},{- 1},1,3} \right\rbrack},\mspace{20mu} {b = {\left\lbrack {{- 3},{- 1},1,3} \right\rbrack*{\exp \left( {j*\frac{1}{3}\pi} \right)}}},\mspace{20mu} {c = {\left\lbrack {{- 3},{- 1},1,3} \right\rbrack*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {P = \begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}}}{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = {k^{th}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}}}}\; \mspace{11mu} \left( {{e.g.},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {{1^{st}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}}}} \right)} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

Normalized codebook sets are represented as follows.

UE index k${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = \begin{matrix}00 & 01 & 10 & 11 \\\left\lbrack {{vec}\mspace{14mu} 1} \right. & {{vec}\mspace{14mu} 2} & {{vec}\mspace{14mu} 3} & {\left. {{vec}\mspace{14mu} 4} \right\rbrack*P_{no}}\end{matrix}$ UE 1 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0 \\{- 3} & {- 1} & 1 & 3\end{bmatrix}*P_{no}$ UE 2 $\begin{bmatrix}{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 3 $\begin{bmatrix}{{- 1}*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} & {{- 3}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} \\{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 4 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 3}*e^{j*\frac{1}{3}\pi}} & {{- 1}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}}\end{bmatrix}*P_{no}$ UE 5 $\begin{bmatrix}{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 3}*e^{j*\frac{1}{3}\pi}} & {{- 1}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}}\end{bmatrix}*P_{no}$ UE 6 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} & {{- 3}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} \\{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ NOTE: P_(no) is (M × M) normalized matrix for thepower constraints, $P_{no} = {\begin{bmatrix}P_{{no},1} & 0 & 0 & 0 \\0 & P_{{no},2} & 0 & 0 \\0 & 0 & P_{{no},3} & 0 \\0 & 0 & 0 & P_{{no},4}\end{bmatrix}.}$ Here, P_(no,m) = (1/|vec m|) × {square root over (K)},for m = 1, . . . , M, where K = 4, M = 4.

Embodiment 2: Optimization of Rules 1 and 3 and Relaxation of Rule 2(Multiple Base Constellation Based Codebook Design)

In Embodiment 2, Rule 1 is optimized for the case where

${{F\left( {{K = 4},{J = 6}} \right)} = \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 0\end{bmatrix}},$

d_(v)=2, and d_(f)=3. In the case, if this factor graph is changed by alinear combination of each column vector or row vector thereof, itscharacteristics are not changed. To optimize Rule 3, the following baseconstellation and phase rotation are proposed.

FIG. 11 illustrates two base constellations.

Referring to FIG. 11, it can be seen that Base Constellation 1: B1=[B₁₁,B₁₂, B₁₃, B₁₄], where B₁₁=−3, B₁₂=−1, B₁₃=1, B₁₄=3, Base Constellation2: B2=[B₂₁, B₂₂, B₂₃, B₂₄], where B₂₁=−3*√{square root over (5)},B₂₂=−1*√{square root over (5)}, B₂₃=*√{square root over (5)}1,B₂₄=3*√{square root over (5)}, and

${{{Phase}\mspace{14mu} {Rotation}\text{:}\mspace{14mu} \theta_{i}} = {\frac{i - 1}{d_{f}}*\pi}},{{{where}\mspace{14mu} i} = 1},{\ldots \mspace{14mu} {d_{f}.}}$

FIG. 12 illustrates mother constellations according to FIG. 11.

Referring to FIG. 12, mother constellations may be configured by baseconstellations 1 and 2 and the phase rotation as follows:

Mother Constellation 1: a=B1*exp(j*θ ₁)=B1=[a(1),a(2),a(3)a(4)]

Mother Constellation 2: b=B2*exp(j*θ₂)=B2*exp(j*⅓π=[b(1),b(2),b(3),b(4)]

Mother Constellation 3: c=B2*exp(j*θ₃)=B2*exp(j*⅔π=[c(1),c(2),c(3),c(4)].

For the optimization of Rule 2, the constellations may be mapped to theUE-specific codebook of each user as follows.

${{{Since}\mspace{20mu} {F\left( {{UE} = 1} \right)}} = \begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 2} \right)}} = \begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 2} = \begin{bmatrix}a \\0 \\{P*c^{T}} \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 3} \right)}} = \begin{bmatrix}1 \\1 \\0 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 3} = \begin{bmatrix}{P*b^{T}} \\a \\0 \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 4} \right)}} = \begin{bmatrix}0 \\0 \\1 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 4} = \begin{bmatrix}0 \\0 \\b \\{P*c^{T}}\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 5} \right)}} = \begin{bmatrix}1 \\0 \\0 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 5} = \begin{bmatrix}{P*c^{T}} \\0 \\0 \\b\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 6} \right)}} = \begin{bmatrix}0 \\1 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 6} = \begin{bmatrix}0 \\{P*b^{T}} \\a \\0\end{bmatrix}},{where}$ $P = {\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.}$

To improve the UE-specific codebook decoding performance of each user,the permutation matrix, P maximizes the Euclidean distance betweencomplex vectors in the UE-specific codebook of each user according toRule 2. For example, assuming that column vectors of

${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {\begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix} = \begin{bmatrix}0 & 0 & 0 & 0 \\{c(2)} & {c(4)} & {c(1)} & {c(3)} \\0 & 0 & 0 & 0 \\{a(1)} & {a(2)} & {a(3)} & {a(4)}\end{bmatrix}}$

are vector 1, 2, 3, and 4, respectively, the phases of vectors 1 and 2are opposite to those of vectors 4 and 3, respectively since c(1)=−c(4),c(2)=−c(3), a(1)=−a(4), and a(2)=−a(3). However, sinceconjugate(c(2))*c(4)+conjugate(a(1))*a(2)≠0 unlike Embodiment 1, vector1 is non-orthogonal to vector 2. Meanwhile, sinceconjugate(c(2))*c(4)+conjugate(b(1))*b(2)=0, UE-specific codebooks 5 and6 are optimized in terms of Rule 2. Regarding Rule 2, UE-specificcodebooks 5 and 6 are optimized, but UE-specific codebooks 1 to 4 maynot be optimized. Thus, the present disclosure proposes a codebookallocation method where UE-specific codebooks 5 and 6 are firstallocated to users, and then remaining UE-specific codebooks 1 to 4 areallocated when NOMA services are provided using the codebooks in uplink.According to this method, the decoding performance of a receiving endmay be further improved.

By substituting the UE-specific codebooks into the factor graph for thebipartite matching obtained from Rule 1, Equation 7 is obtained.

$\begin{matrix}{{F\left( {{K = 4},{J = 6}} \right)} = \left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

Meanwhile, in Rule 3, the superposition of constellations (i, j, k) mayhave a total of M^(d) ^(f) (4³=64) combinations according to the motherconstellations and the bipartite matching as shown in FIG. 13.

FIG. 13 illustrates superposition of constellations.

In FIG. 13, the x axis corresponds to the real domain of theconstellation superposition, and the y axis corresponds to the imaginarydomain of the constellation superposition. In FIG. 13, it can be seenfrom superposition of constellation patterns that each of the 64constellations has a predetermined Euclidean distance withoutsuperposition. That is, an almost optimized Euclidean distance may bedesigned in Rule 3 regardless combination of traffic of each user. Theentire codebook may be summarized as shown in Equation 8.

$\begin{matrix}{{{F\left( {{K = 4},{J = 6}} \right)} = \left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack}\mspace{20mu} {{{a = \left\lbrack {{- 3},{- 1},1,3} \right\rbrack},{b = {\left\lbrack {{{- 3}*\sqrt{5}},{{- 1}*\sqrt{5}},{1*\sqrt{5}},{3*\sqrt{5}}} \right)*{\exp \left( {j*\frac{3}{2}\pi} \right)}}},{c = {\left\lbrack {{{- 3}*\sqrt{5}},{{- 1}*\sqrt{5}},{1*\sqrt{5}},{3*\sqrt{5}}} \right)*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {P = \begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}}}{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = {k^{th}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}\mspace{11mu} \left( {{e.g.},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {{1^{st}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}}}} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

Normalized codebook sets are represented as follows.

UE index k${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = \begin{matrix}00 & 01 & 10 & 11 \\\left\lbrack {{vec}\mspace{14mu} 1} \right. & {{vec}\mspace{14mu} 2} & {{vec}\mspace{14mu} 3} & {\left. {{vec}\mspace{14mu} 4} \right\rbrack*P_{no}}\end{matrix}$ UE 1 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- \sqrt{5}}*e^{j*\frac{2}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {{- 3}\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {\sqrt{5}*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0 \\{- 3} & {- 1} & 1 & 3\end{bmatrix}*P_{no}$ UE 2 $\begin{bmatrix}{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0 \\{{- \sqrt{5}}*e^{j*\frac{2}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {{- 3}\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {\sqrt{5}*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 3 $\begin{bmatrix}{{- \sqrt{5}}*e^{j*\frac{1}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{1}{3}\pi}} & {{- 3}\sqrt{5}*e^{j*\frac{1}{3}\pi}} & {\sqrt{5}*e^{j*\frac{1}{3}\pi}} \\{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 4 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 3}\sqrt{5}*e^{j*\frac{1}{3}\pi}} & {{- \sqrt{5}}*e^{j*\frac{1}{3}\pi}} & {\sqrt{5}*e^{j*\frac{1}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{1}{3}\pi}} \\{{- \sqrt{5}}*e^{j*\frac{2}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {{- 3}\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {\sqrt{5}*e^{j*\frac{2}{3}\pi}}\end{bmatrix}*P_{no}$ UE 5 $\begin{bmatrix}{{- \sqrt{5}}*e^{j*\frac{2}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {{- 3}\sqrt{5}*e^{j*\frac{2}{3}\pi}} & {\sqrt{5}*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 3}\sqrt{5}*e^{j*\frac{1}{3}\pi}} & {{- \sqrt{5}}*e^{j*\frac{1}{3}\pi}} & {\sqrt{5}*e^{j*\frac{1}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{1}{3}\pi}}\end{bmatrix}*P_{no}$ UE 6 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- \sqrt{5}}*e^{j*\frac{1}{3}\pi}} & {3\sqrt{5}*e^{j*\frac{3}{3}\pi}} & {{- 3}\sqrt{5}*e^{j*\frac{1}{3}\pi}} & {\sqrt{5}*e^{j*\frac{1}{3}\pi}} \\{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ NOTE: P_(no) is (M × M) normalized matrix for thepower constraints. $P_{no} = {\begin{bmatrix}P_{{no},1} & 0 & 0 & 0 \\0 & P_{{no},2} & 0 & 0 \\0 & 0 & P_{{no},3} & 0 \\0 & 0 & 0 & P_{{no},4}\end{bmatrix}.}$ Here, P_(no,m) = (1/|vec m|) × {square root over (K)},for m = 1, . . . , M, where K = 4, M = 4.

Embodiment 3: Optimization of Rules 1 and 4 and Relaxation of Rules 2and 3 (Asymmetric Base Constellation Based Codebook Design)

In Embodiment 3, Rule 1 is optimized for the case where

${{F\left( {{K = 4},{J = 6}} \right)} = \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 0\end{bmatrix}},$

d_(v)=2, and d_(f)=3. In the case, if this factor graph is changed by alinear combination of each column vector or row vector thereof, itscharacteristics are not changed. To optimize Rule 4, the followingsingle asymmetric base constellation and phase rotation are proposed.

FIG. 14 illustrates a single asymmetric base constellation.

Referring to FIG. 14, it can be seen that Asymmetric Base Constellation:B=[B₁, B₂, B₃, B₄], where B₁=−4 B₂=−1, B₃=2, B₄=5 and

${{{Phase}\mspace{14mu} {Rotation}\text{:}\mspace{14mu} \theta_{i}} = {\frac{i - 1}{d_{f}}*2\; \pi}},{{{where}\mspace{14mu} i} = 1},{\ldots \mspace{14mu} {d_{f}.}}$

Then, mother constellations may be configured by the asymmetric baseconstellation and phase rotation as shown in FIG. 15.

FIG. 15 illustrates mother constellations according to FIG. 14.

Mother Constellation 1: a=B*exp(j*θ ₁)=B=[a(1),a(2),a(3)a(4)]

Mother Constellation 2: b=B*exp(j*θ ₂)=B*exp(j*⅔π=[b(1),b(2),b(3),b(4)]

Mother Constellation 3: c=B*exp(j*θ ₃)=B*exp(j*4/3π=[c(1),c(2),c(3),c(4)].

That is, the Euclidean distance between the mother constellations isoptimized. However, in this case, the Euclidean distance is notoptimized for all constellations, but the Euclidean distance isoptimized between the most dominant inner constellations when theconstellations are configured using an ML approach. The Euclideandistance between constellations may be considered to be optimized ifthere is no constellation superposition on a single resource formultiple users.

For the optimization of Rule 2, the constellations may be mapped to theUE-specific codebook of each user as follows.

${{{Since}\mspace{20mu} {F\left( {{UE} = 1} \right)}} = \begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 2} \right)}} = \begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 2} = \begin{bmatrix}a \\0 \\{P*c^{T}} \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 3} \right)}} = \begin{bmatrix}1 \\1 \\0 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 3} = \begin{bmatrix}{P*b^{T}} \\a \\0 \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 4} \right)}} = \begin{bmatrix}0 \\0 \\1 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 4} = \begin{bmatrix}0 \\0 \\b \\{P*c^{T}}\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 5} \right)}} = \begin{bmatrix}1 \\0 \\0 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 5} = \begin{bmatrix}{P*c^{T}} \\0 \\0 \\b\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{20mu} {F\left( {{UE} = 6} \right)}} = \begin{bmatrix}0 \\1 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 6} = \begin{bmatrix}0 \\{P*b^{T}} \\a \\0\end{bmatrix}},{where}$ $P = {\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.}$

To improve the UE-specific codebook decoding performance of each user,the permutation matrix, P maximizes the Euclidean distance betweencomplex vectors in the UE-specific codebook of each user according toRule 2. For example, assuming that column vectors of

${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {\begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix} = \begin{bmatrix}0 & 0 & 0 & 0 \\{c(2)} & {c(4)} & {c(1)} & {c(3)} \\0 & 0 & 0 & 0 \\{a(1)} & {a(2)} & {a(3)} & {a(4)}\end{bmatrix}}$

are vector 1, 2, 3, and 4, respectively, there is no phase reversalbetween vectors since c(1)≠−c(4), c(2)−c(3), a(1)≠−a(4), and a(2)≠−a(3).In addition, since conjugate(c(2))*c(4)+conjugate(a(1))*a(2)≠0 unlikeEmbodiment 1, vector 1 is non-orthogonal to vector 2. As a result, theUE-specific codebooks may not be optimized. However, each vector has aEuclidean distance close to a near-orthogonal relationship and a phaseinverse relationship. By substituting the UE-specific codebooks into thefactor graph for the bipartite matching obtained from Rule 1, Equation 9is obtained.

$\begin{matrix}{{F\left( {{K = 4},{J = 6}} \right)} = \left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

Meanwhile, in Rule 3, the superposition of constellations (i, j, k) mayhave a total of M^(d) ^(f) (4³=64) combinations according to the motherconstellations and the bipartite matching. However, the superposition ofconstellations may not be optimized as in Embodiment 1. The entirecodebook may be summarized as shown in Equation 10.

$\begin{matrix}{{F\left( {{K = 4},{J = 6}} \right)} = {\quad{{{\left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack \mspace{20mu} a} = \left\lbrack {{- 4},{- 1},2,5} \right\rbrack},\mspace{20mu} {b = {\left\lbrack {{- 4},{- 1},2,5} \right\rbrack*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {c = {\left\lbrack {{- 4},{- 1},2,5} \right\rbrack*{\exp \left( {j*\frac{4}{3}\pi} \right)}}},\mspace{20mu} {P = {{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = {k^{th}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}\mspace{14mu} \left( {{e.g.},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {{1^{st}{column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}}}} \right)}}}}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

Normalized codebook sets are represented as follows.

UE index k${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = \begin{matrix}00 & 01 & 10 & 11 \\\left\lbrack {{vec}\mspace{14mu} 1} \right. & {{vec}\mspace{14mu} 2} & {{vec}\mspace{14mu} 3} & {\left. {{vec}\mspace{14mu} 4} \right\rbrack*P_{no}}\end{matrix}$ UE 1 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{4}{3}\pi}} & {5*e^{j*\frac{4}{3}\pi}} & {{- 4}*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}} \\0 & 0 & 0 & 0 \\{- 4} & {- 1} & 2 & 5\end{bmatrix}*P_{no}$ UE 2 $\begin{bmatrix}{- 4} & {- 1} & 2 & 5 \\0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{4}{3}\pi}} & {5*e^{j*\frac{4}{3}\pi}} & {{- 4}*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}} \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 3 $\begin{bmatrix}{{- 1}*e^{j*\frac{2}{3}\pi}} & {5*e^{j*\frac{2}{3}\pi}} & {{- 4}*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} \\{- 4} & {- 1} & 2 & 5 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 4 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 4}*e^{j*\frac{2}{3}\pi}} & {{- 1}*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} & {5*e^{j*\frac{2}{3}\pi}} \\{{- 1}*e^{j*\frac{4}{3}\pi}} & {5*e^{j*\frac{4}{3}\pi}} & {{- 4}*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}}\end{bmatrix}*P_{no}$ UE 5 $\begin{bmatrix}{{- 1}*e^{j*\frac{4}{3}\pi}} & {5*e^{j*\frac{4}{3}\pi}} & {{- 4}*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 4}*e^{j*\frac{2}{3}\pi}} & {{- 1}*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} & {5*e^{j*\frac{2}{3}\pi}}\end{bmatrix}*P_{no}$ UE 6 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {5*e^{j*\frac{2}{3}\pi}} & {{- 4}*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} \\{- 4} & {- 1} & 2 & 5 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ NOTE: P_(no) is (M × M) normalized matrix for thepower constraints, $P_{no} = {\begin{bmatrix}P_{{no},1} & 0 & 0 & 0 \\0 & P_{{no},2} & 0 & 0 \\0 & 0 & P_{{no},3} & 0 \\0 & 0 & 0 & P_{{no},4}\end{bmatrix}.}$ Here, P_(no,m) = (1/|vec m|) × {square root over (K)},for m = 1, . . . , M, where K = 4, M = 4.

Embodiment 4: Optimization of Rules 1 and 4 and Relaxation of Rules 2and 3 (Asymmetric 2D Base Constellation Based Codebook Design)

Rule 1 is optimized for the case where

${{F\left( {{K = 4},{J = 6}} \right)} = \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 \\1 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 1 & 0\end{bmatrix}},$

d_(v)=2, and d_(f)=3. In the case, if this factor graph is changed by alinear combination of each column vector or row vector thereof, itscharacteristics are not changed. To optimize Rule 4, the followingasymmetric 2D base constellation and phase rotation are proposed.

FIG. 16 illustrates an asymmetric 2D base constellation.

In FIG. 16,

Asymmetric  2D  Base  Constellation  :  B = [B₁, B₂, B₃, B₄], where${B_{1} = {{- 2.5} - {\frac{\sqrt{3}}{2}i}}},{B_{2} = {- 1}},{B_{3} = 2},{B_{4} = {3.5 + {\frac{\sqrt{3}}{2}i}}},{and}$${{{Phase}\mspace{14mu} {{Rotation}:\theta_{i}}} = {\frac{i - 1}{d_{f}}*2\; \pi}},{{{where}\mspace{14mu} i} = 1},{\ldots \mspace{20mu} {d_{f}.}}$

Then, mother constellations may be configured by the asymmetric 2D baseconstellation and phase rotation as follows.

FIG. 17 illustrates mother constellations according to FIG. 16.

Mother Constellation 1: a=B*exp(j*θ ₁)=B=[a(1),a(2),a(3)a(4)]

Mother Constellation 2: b=B*exp(j*θ ₂)=B*exp(j*⅔π=[b(1),b(2),b(3),b(4)]

Mother Constellation 3: c=B*exp(j*θ ₃)=B*exp(j*4/3π=[c(1),c(2),c(3),c(4)].

That is, the Euclidean distance between the mother constellations isoptimized. Unlike Embodiment 3, the Euclidean distance is optimized forall constellations. Specifically, the Euclidean distance is optimizedfor all constellations when the constellations are configured using anML approach. The Euclidean distance between constellations may beconsidered to be optimized if there is no constellation superposition ona single resource for multiple users.

For the optimization of Rule 2, the constellations may be mapped to theUE-specific codebook of each user as follows.

${{{Since}\mspace{14mu} {F\left( {{UE} = 1} \right)}} = \begin{bmatrix}0 \\1 \\0 \\1\end{bmatrix}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{14mu} {F\left( {{UE} = 2} \right)}} = \begin{bmatrix}1 \\0 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 2} = \begin{bmatrix}a \\0 \\{P*c^{T}} \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{14mu} {F\left( {{UE} = 3} \right)}} = \begin{bmatrix}1 \\1 \\0 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 3} = \begin{bmatrix}{P*b^{T}} \\a \\0 \\0\end{bmatrix}},{where}$ ${P = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{14mu} {F\left( {{UE} = 4} \right)}} = \begin{bmatrix}0 \\0 \\1 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 4} = \begin{bmatrix}0 \\0 \\b \\{P*c^{T}}\end{bmatrix}},{{{where}P} = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{14mu} {F\left( {{UE} = 5} \right)}} = \begin{bmatrix}1 \\0 \\0 \\1\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 5} = \begin{bmatrix}{P*c^{T}} \\0 \\0 \\b\end{bmatrix}},{{{where}P} = {{{\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.{Since}}\mspace{14mu} {F\left( {{UE} = 6} \right)}} = \begin{bmatrix}0 \\1 \\1 \\0\end{bmatrix}}},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 6} = \begin{bmatrix}0 \\{P*b^{T}} \\a \\0\end{bmatrix}},{where}$ $P = {\begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}.}$

To improve the UE-specific codebook decoding performance of each user,the permutation matrix, P maximizes the Euclidean distance betweencomplex vectors in the UE-specific codebook of each user according toRule 2. For example, assuming that column vectors of

${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {\begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix} = \begin{bmatrix}0 & 0 & 0 & 0 \\{c(2)} & {c(4)} & {c(1)} & {c(3)} \\0 & 0 & 0 & 0 \\{a(1)} & {a(2)} & {a(3)} & {a(4)}\end{bmatrix}}$

are vector 1, 2, 3, and 4, respectively, there is no phase reversalbetween vectors since c(1)≠c(4), c(2)≠−c(3), a(1)≠−a(4), and a(2)≠−a(3).In addition, since conjugate(c(2))*c(4)+conjugate(a(1))*a(2)≠0 unlikeEmbodiment 1, vector 1 is non-orthogonal to vector 2. As a result, theUE-specific codebooks may not be optimized. However, each vector has aEuclidean distance close to a near-orthogonal relationship and a phaseinverse relationship. By substituting the UE-specific codebooks into thefactor graph for the bipartite matching obtained from Rule 1, Equation11 is obtained.

$\begin{matrix}{{F\left( {{K = 4},{J = 6}} \right)} = \left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

Meanwhile, in Rule 3, the superposition of constellations (i, j, k) mayhave a total of M^(d) ^(f) (4³=64) combinations according to the motherconstellations and the bipartite matching. However, the superposition ofconstellations may not be optimized as in Embodiment 1. The entirecodebook may be summarized as follows.

${F\left( {{K = 4},{J = 6}} \right)} = \left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & {P*c^{T}} & 0 & b & 0 & a \\a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack$$\mspace{20mu} {{a = \left\lbrack {{{- 2.5} - {\frac{\sqrt{3}}{2}i}},{- 1},2,{3.5 + {\frac{\sqrt{3}}{2}i}}} \right\rbrack},\mspace{20mu} {b = {\left\lbrack {{{- 2.5} - {\frac{\sqrt{3}}{2}i}},{- 1},2,{3.5 + {\frac{\sqrt{3}}{2}i}}} \right\rbrack*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {c = {\left\lbrack {{{- 2.5} - {\frac{\sqrt{3}}{2}i}},{- 1},2,{3.5 + {\frac{\sqrt{3}}{2}i}}} \right\rbrack*{\exp \left( {j*\frac{4}{3}\pi} \right)}}},\mspace{20mu} {P = \begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}}}$${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = {k^{th}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}\mspace{14mu} \left( {{e.g.},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {{1^{st}\mspace{20mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}} = \begin{bmatrix}0 \\{P*c^{T}} \\0 \\a\end{bmatrix}}}} \right)}$

In Rule 3, the superposition of constellations (i, j, k) may have atotal of M^(d) ^(f) (4³=64) combinations according to the motherconstellations and the bipartite matching. However, the superposition ofconstellations may not be optimized as in Embodiment 1. The entirecodebook may be summarized as follows.

Normalized codebook sets are represented as follows.

UE index k${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = \begin{matrix}00 & 01 & 10 & 11 \\\left\lbrack {{vec}\mspace{14mu} 1} \right. & {{vec}\mspace{14mu} 2} & {{vec}\mspace{14mu} 3} & {\left. {{vec}\mspace{14mu} 4} \right\rbrack*P_{no}}\end{matrix}$ UE 1 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{4}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {\left( {{- 2.5} - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}} \\0 & 0 & 0 & 0 \\{{- 2.5} - {\frac{\sqrt{3}}{2}i}} & {- 1} & 2 & {3.5 + {\frac{\sqrt{3}}{2}i}}\end{bmatrix}*P_{no}$ UE 2 $\begin{bmatrix}{{- 2.5} - {\frac{\sqrt{3}}{2}i}} & {- 1} & 2 & {3.5 + {\frac{\sqrt{3}}{2}i}} \\0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{4}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {\left( {{- 2.5} - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}} \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 3 $\begin{bmatrix}{{- 1}*e^{j*\frac{2}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}} & {\left( {{- 2.5} - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} \\{{- 2.5} - {\frac{\sqrt{3}}{2}i}} & {- 1} & 2 & {3.5 + {\frac{\sqrt{3}}{2}i}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 4 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{\left( {2.5 - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}} & {{- 1}*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}} \\{{- 1}*e^{j*\frac{4}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {\left( {{- 2.5} - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}}\end{bmatrix}*P_{no}$ UE 5 $\begin{bmatrix}{{- 1}*e^{j*\frac{4}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {\left( {{- 2.5} - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{4}{3}\pi}} & {2*e^{j*\frac{4}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{\left( {{- 2.5} - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}} & {{- 1}*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}}\end{bmatrix}*P_{no}$ UE 6 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {\left( {3.5 + {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}} & {\left( {{- 2.5} - {\frac{\sqrt{3}}{2}i}} \right)*e^{j*\frac{2}{3}\pi}} & {2*e^{j*\frac{2}{3}\pi}} \\{{- 2.5} - {\frac{\sqrt{3}}{2}i}} & {- 1} & 2 & {3.5 + {\frac{\sqrt{3}}{2}i}} \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ NOTE: P_(no) is (M × M) normalized matrix for thepower constraints, $P_{no} = {\begin{bmatrix}P_{{no},1} & 0 & 0 & 0 \\0 & P_{{no},2} & 0 & 0 \\0 & 0 & P_{{no},3} & 0 \\0 & 0 & 0 & P_{{no},4}\end{bmatrix}.}$ Here, P_(no,m) = (1/|vec m|) × {square root over (K)},for m = 1, . . . , M, where K = 4, M = 4.

Embodiment 5: Codebook Extension in Accordance with Rule 5

Hereinafter, a case in which the bipartite matching rule is extended toprovide high connectivity will be described. As described in Rule 5, thefactor graph of the bipartite matching obtained in Embodiment 1, 2, 3 or4 is extended by the Cartesian product with an identity matrix.

For example, since

${{F\left( {{K = 8},{J = 12}} \right)} = {{I_{2 \times 2} \times {F\left( {{K = 4},{J = 6}} \right)}} = \left\lbrack \begin{matrix}{F\left( {{K = 4},{J = 6}} \right)} & 0 \\0 & {F\left( {{K = 4},{J = 6}} \right)}\end{matrix} \right\rbrack}},{F\left( {{K = 8},{J = 12}} \right)}$

may be extended as follows:

${F\left( {{K = 8},{J = 12}} \right)} = {\left\lbrack \begin{matrix}0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\{P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & {P*c^{T}} & 0 & b & 0 & a & 0 & 0 & 0 & 0 & 0 & 0 \\a & 0 & 0 & {P*c^{T}} & b & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & a & {P*b^{T}} & 0 & {P*c^{T}} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {P*c^{T}} & 0 & a & 0 & 0 & {P*b^{T}} \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {P*c^{T}} & 0 & b & 0 & a \\0 & 0 & 0 & 0 & 0 & 0 & a & 0 & 0 & {P*c^{T}} & b & 0\end{matrix} \right\rbrack.}$

Similarly, the following extension of

${F\left( {{mk},{mJ}} \right)} = {{I_{m \times m} \times {F\left( {K,J} \right)}} = \begin{bmatrix}{F\left( {K,J} \right)} & \ldots & 0 \\\vdots & \ddots & \vdots \\0 & \cdots & {F\left( {K,J} \right)}\end{bmatrix}}$

may be established.

By doing so, as the values of J and K increase, a larger factor graphmay be used for the bipartite matching. In this case, although thedecoding complexity of a receiving end may linearly increase, the factorgraph of the bipartite matching may be extended without degradation ofthe decoding performance. The above-described codebook extension may bedirectly applied to Embodiment 1, 2, 3, or 4. When normalized codebooksets are configured, normalized values may be changed depending on thevalue of K.

Embodiment 6: Design of Codebook with K=6 and J=9 According toEmbodiment 1, 2,3, or 4

Regarding the above-described codebook design, Embodiment 1, 2, or 3 maybe equally applied when

${{F\left( {{K = 6},{J = 9}} \right)} = \begin{bmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1\end{bmatrix}},$

d_(v)=2, and d_(f)=3 due to an increase in the value of K. However, inthe case of K=6, the maximum factor graph for maintaining that d_(v)=2is

${F\left( {{K = 6},{J = 15}} \right)} = \begin{bmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0\end{bmatrix}$

and d_(f)=5. Thus, the number of possibilities of selecting 9 columnvectors from such that the condition of d_(f)=3 is satisfied may bevarious. However, it may be equally applied to Embodiment 1, 2, 3, or 4regardless of which combination of column vectors is selected. Assumingthat the codebook is designed such that

${{F\left( {{K = 6},{J = 9}} \right)} = \begin{bmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1\end{bmatrix}},$

the entire codebook may be designed using the base constellation andphase rotation illustrated in Embodiments 1 and 2 as shown in Equation12.

$\begin{matrix}{{F\left( {{K = 6},{J = 9}} \right)} = \left\lbrack \begin{matrix}a & b & {P*c^{T}} & 0 & 0 & 0 & 0 & 0 & 0 \\{P*b^{T}} & 0 & 0 & {P*c^{T}} & a & 0 & 0 & 0 & 0 \\0 & {P*c^{T}} & 0 & b & 0 & a & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {P*b^{T}} & 0 & a & {P*c^{T}} & 0 \\0 & 0 & a & 0 & 0 & 0 & {P*c^{T}} & 0 & b \\0 & 0 & 0 & 0 & 0 & {P*b^{T}} & 0 & a & {P*c^{T}}\end{matrix} \right\rbrack} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

The methods in Embodiments 1 to 4 may be represented as follows.

$\mspace{20mu} {{{{Method}\mspace{14mu} {in}\mspace{14mu} {Embodiment}{\; \mspace{11mu}}1\text{:}\mspace{11mu} a} = \left\lbrack {{- 3},{- 1},1,3} \right\rbrack},\mspace{20mu} {b = {\left\lbrack {{- 3},{- 1},1,3} \right\rbrack*{\exp \left( {j*\frac{3}{2}\pi} \right)}}},\mspace{20mu} {c = {\left\lbrack {{- 3},{- 1},1,3} \right\rbrack*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {P = \begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}}}$$\mspace{20mu} {{{{Method}\mspace{14mu} {in}\mspace{14mu} {Embodiment}{\; \mspace{11mu}}2\text{:}\mspace{11mu} a} = \left\lbrack {{- 3},{- 1},1,3} \right\rbrack},\mspace{20mu} {b = {\left\lbrack {{{- 3}*\sqrt{5}},{{- 1}*\sqrt{5}},{1*\sqrt{5}},{3*\sqrt{5}}} \right\rbrack*{\exp \left( {j*\frac{3}{2}\pi} \right)}}},\mspace{20mu} {c = {\left\lbrack {{{- 3}*\sqrt{5}},{{- 1}*\sqrt{5}},{1*\sqrt{5}},{3*\sqrt{5}}} \right\rbrack*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {P = \begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}}}$$\mspace{20mu} {{{{Method}\mspace{14mu} {in}\mspace{14mu} {Embodiment}{\; \mspace{11mu}}3\text{:}\mspace{11mu} a} = \left\lbrack {{- 4},{- 1},2,5} \right\rbrack},\mspace{20mu} {b = {\left\lbrack {{- 4},{- 1},2,5} \right\rbrack*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {c = {\left\lbrack {{- 4},{- 1},2,5} \right\rbrack*{\exp \left( {j*\frac{3}{2}\pi} \right)}}},\mspace{20mu} {P = \begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}}}$   Method  in  Embodiment   4:  $\mspace{20mu} {{a = \left\lbrack {{{- 2.5} - {\frac{\sqrt{3}}{2}i}},{- 1},2,{3.5 + {\frac{\sqrt{3}}{2}i}}} \right\rbrack},\mspace{20mu} {b = {\left\lbrack {{{- 2.5} - {\frac{\sqrt{3}}{2}i}},{- 1},2,{3.5 + {\frac{\sqrt{3}}{2}i}}} \right\rbrack*{\exp \left( {j*\frac{2}{3}\pi} \right)}}},\mspace{20mu} {c = {\left\lbrack {{{- 2.5} - {\frac{\sqrt{3}}{2}i}},{- 1},2,{3.5 + {\frac{\sqrt{3}}{2}i}}} \right\rbrack*{\exp \left( {j*\frac{4}{3}\pi} \right)}}},\mspace{20mu} {P = \begin{bmatrix}0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0\end{bmatrix}}}$${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = {k^{th}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}\mspace{14mu} \left( {{e.g.},{{{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} 1} = {{1^{st}\mspace{14mu} {column}\mspace{14mu} {of}\mspace{14mu} F\mspace{14mu} {matrix}} = \begin{bmatrix}a \\{P*b^{T}} \\0 \\0 \\0 \\0\end{bmatrix}}}} \right)}$

In Embodiment 1, the normalized codebook sets may be represented asfollows.

UE index k${{UE}\mspace{14mu} {specific}\mspace{14mu} {Codebook}\mspace{14mu} k} = \begin{matrix}00 & 01 & 10 & 11 \\\left\lbrack {{vec}\mspace{14mu} 1} \right. & {{vec}\mspace{14mu} 2} & {{vec}\mspace{14mu} 3} & {\left. {{vec}\mspace{14mu} 4} \right\rbrack*P_{no}}\end{matrix}$ UE 1 $\begin{bmatrix}{- 3} & {- 1} & 1 & 3 \\{{- 1}*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} & {{- 3}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 2 $\begin{bmatrix}{{- 3}*e^{j*\frac{1}{3}\pi}} & {{- 1}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} \\0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 3 $\begin{bmatrix}{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 4 $\begin{bmatrix}0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\{{- 3}*e^{j*\frac{1}{3}\pi}} & {{- 1}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 5 $\begin{bmatrix}0 & 0 & 0 & 0 \\{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} & {{- 3}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 6 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{- 3} & {- 1} & 1 & 3 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{1*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} & {{- 3}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}}\end{bmatrix}*P_{no}$ UE 7 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{- 3} & {- 1} & 1 & 3 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0\end{bmatrix}*P_{no}$ UE 8 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}} \\0 & 0 & 0 & 0 \\{- 3} & {- 1} & 1 & 3\end{bmatrix}*P_{no}$ UE 9 $\begin{bmatrix}0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\{{- 3}*e^{j*\frac{1}{3}\pi}} & {{- 1}*e^{j*\frac{1}{3}\pi}} & {1*e^{j*\frac{1}{3}\pi}} & {3*e^{j*\frac{1}{3}\pi}} \\{{- 1}*e^{j*\frac{2}{3}\pi}} & {3*e^{j*\frac{2}{3}\pi}} & {{- 3}*e^{j*\frac{2}{3}\pi}} & {1*e^{j*\frac{2}{3}\pi}}\end{bmatrix}*P_{no}$ NOTE: P_(no) is (M × M) normalized matrix for thepower constraints, $P_{no} = {\begin{bmatrix}P_{{no},1} & 0 & 0 & 0 \\0 & P_{{no},2} & 0 & 0 \\0 & 0 & P_{{no},3} & 0 \\0 & 0 & 0 & P_{{no},4}\end{bmatrix}.}$ Here, P_(no,m) = (1/|vec m|) × {square root over (K)},for m = 1, . . . , M, where K = 6, M = 4.

FIG. 18 illustrates the performance of an MPA decoder according toEmbodiments 1, 2, 3, and 4.

In FIG. 18, the reference system corresponds to a result obtained byusing a conventional codebook, and Types A, B, C, and D correspond toresults obtained by using Embodiments 1, 2, 3, and 4, respectively. Theresult shows a symbol error rate (SER) in an additive white Gaussiannoise (AWGN) environment in a multiuser superposition access systemusing the codebooks in Embodiments 1, 2, 3, and 4. It can be seen thatthe codebooks proposed in the present disclosure have better performancethan predefined codebooks computed by computer simulation.

In all of the above-described embodiments, a codebook may be generatedusing not only a single embodiment but also a combination thereof. Forexample, a codebook may be designed based on asymmetric multiple baseconstellations obtained by combining the asymmetric base constellationof Embodiment 3 and the multiple base constellations of Embodiment 2. Inall of the embodiments and examples, a codeword corresponding to acolumn vector of a codebook used by a transmitting end is normalized bytransmission power. However, the codebook design methods described inthe embodiments are not limited thereto. That is, other combinationresults (e.g., a linear combination of factor graphs, linear scaling ofa mother constellation, etc.) may be obtained using the same designmethods.

Signal Flow for MM-based NOMA

Regarding the codebooks proposed in the above-described embodiments, amethod of exchanging and signaling information on a codebook is requiredfor MM-based NOMA. Accordingly, methods of exchanging and signalinginformation on a codebook for MM-based NOMA proposed in the codebookdesign embodiments will be described hereinafter.

FIG. 19 illustrates a method of exchanging and signaling information ona codebook for MM-based NOMA in downlink scheduling based transmission,and FIG. 20 illustrates a method of exchanging and signaling informationon a codebook for MM-based NOMA in uplink scheduling based transmission.

Referring to FIGS. 19 and 20, it can be seen that information on theindex of a UE-specific codebook is signaled through control signaling orover a control channel FIGS. 19 and 20 show downlink signal flow anduplink signal flow in an MM-based NOMA system, respectively. An eNB anda UE may have information on a predefined MM-based codebook set. TheMM-based codebook set information may correspond to a set of UE-specificcodebooks, and the codebooks proposed in the present disclosure may beused as the UE-specific codebooks. In this case, the eNB and UE may usevarious methods to have the information on the predefined MM-basedcodebook set. For example, 1) the eNB and UE may store the entirety ofthe MM-based codebook set predetermined therebetween by offline, or 2)the UE may receive the entirety of the MM-base codebook set through RRCsignaling during an initial access procedure, an RRC procedure, etc.

Referring to FIG. 19, the eNB may perform MM-based encoding based on aUE-specific codebook (e.g., a specific codebook among the codebooksproposed in the present disclosure). The eNB may transmit to the UE adownlink control channel (e.g., xPDCCH) including information on aUE-specific codebook index, an MCS (modulation and coding scheme) index,and the like selected for the corresponding UE. In addition, the eNB maytransmit to the corresponding UE a downlink data channel based on thedownlink control channel. The UE may detect downlink data using a MUDscheme based on the information included in the received downlinkcontrol channel and then transmit ACK/NACK for the downlink data channelto the eNB.

Referring to FIG. 20, the eNB may transmit to the UE a downlink controlchannel (e.g., xPDCCH) including information on a UE-specific codebookindex, an MCS index, and the like selected for the corresponding UE. TheUE may perform MM-based encoding based on a UE-specific codebook (e.g.,a specific codebook among the codebooks proposed in the presentdisclosure) and transmit an uplink data channel (e.g., xPUSCH) based onthe received downlink control channel. The eNB may detect the uplinkdata channel using a MUD scheme and then transmit ACK/NACK for theuplink data channel to the UE.

FIG. 21 illustrates a method of exchanging and signaling information ona codebook for MM-based NOMA in downlink scheduling based transmission,and FIG. 22 illustrates a method of exchanging and signaling informationon a codebook for MM-based NOMA in uplink scheduling based transmission.

FIGS. 21 and 22 are different from FIGS. 19 and 20 in that the eNBtransmits a UE-specific codebook index for the UE but also an entireMM-based codebook set over a downlink control channel FIGS. 19 and 20assume that the entire MM-based codebook set is shared by the eNB and UEthrough an initial access procedure or via RRC signaling, but FIGS. 21and 22 assume that the entire MM-based codebook set is transmitted bythe eNB to the UE over a downlink control channel.

When there is a request for downlink and uplink informationtransmission, an eNB transmits to a UE a codebook index corresponding toa UE-specific codebook to be used by the corresponding UE throughfairness scheduling. The UE uses the UE-specific codebook for modulationor demodulation based on the received codebook index. In this case, thenumber of codebooks allocated to the corresponding UE may be one or twoor more. Specifically, if the UE requires a high data transfer rate, twoor more symbols may be simultaneously transmitted using two or morecodebooks, and the two or more symbols may be demodulated by a receivingend. In addition, the values of J and K which determine the dimension ofa codebook may be changed according to the system environment. Thecodebook that depends on the values of J and K may be generated orpredefined according to the methods described in the codebook-relatedembodiments.

The eNB may perform resource management based on the fairnessscheduling. That is, the eNB may determine an MCS level based on thevalue of MUI, which depends on the codebook characteristics, or anexpected demodulation error rate. Then, the eNB may perform the fairnessscheduling based on the determined MCS level.

Contention-based Transmission

FIGS. 23 and 24 illustrate contention-based transmission in an MM-basedNOMA system. Specifically, FIG. 23 illustrates signal flow in acontention-based transmission system based on UE-specific codebookallocation, and FIG. 24 illustrates signal flow in a contention-basedtransmission system based on UE-specific codebook selection.

FIG. 23 shows a case in which an eNB pre-allocates a UE-specificcodebook for contention-based transmission in the MM-based NOMA system,and FIG. 24 shows a case in which a UE selects a UE-specific codebookfor contention-based transmission in the MM-based NOMA system. In thiscase, the eNB and UE may have information on a predefined MM-basedcodebook set. The MM-based codebook set information may correspond to aset of UE-specific codebooks, and the codebooks proposed in the presentdisclosure may be used as the UE-specific codebooks. In addition, theeNB and UE may use various methods to have the information on thepredefined MM-based codebook set. For example, 1) the eNB and UE maystore the entirety of the MM-based codebook set predeterminedtherebetween by offline, or 2) the UE may receive the entirety of theMM-base codebook set through RRC signaling during an initial accessprocedure, an RRC procedure, etc.

In this case, the UE may receive information for contention-basedtransmission (e.g., an MCS, a contention resource zone, power control,etc. for the contention-based transmission) via RRC signaling orperiodic control signaling. Referring to FIG. 23, the UE may receivefrom the eNB information on a UE-specific codebook index allocated forthe corresponding UE, an MCS index (or MCS level), a contention zone forcontention-based transmission, etc. The UE may perform MM-based encodingbased on a UE-specific codebook corresponding to the UE-specificcodebook index allocated for the UE. Thereafter, the UE may perform thecontention-based transmission using an uplink data channel or acontention resource zone.

Referring to FIG. 24, when no UE-specific codebook index ispre-allocated, the UE may select a UE-specific codebook index accordingto a predetermined rule and perform MM-based encoding based on aUE-specific codebook corresponding to the selected UE-specific codebookindex. Thereafter, the UE may perform contention-based transmissionusing an uplink data channel or a contention resource zone. To select aUE-specific codebook index, various methods such as (1) a method ofselecting a random UE-specific codebook from a UE-specific codebook setand (2) a method of selecting a UE-specific codebook based on aUE-specific codebook index (k)=mod (C-RNTI(k), Maximum Codebook Index)may be used. The eNB may decode a received signal by performing MUDbased on blind detection without knowing which UE transmits the signalin a contention zone. In this case, the eNB may know the UE thattransmits the signal using a CRC check in the decoded signal and C-RNTIinformation in the decoded data.

Although the present disclosure is described based on DL transmission ina cellular system, the disclosure is also applicable to all systemsusing multiuser access technology, for example, UL transmission in thecellular system, machine type communication (MTC), device-to-device(D2D) communication, vehicle-to-everything (V2X) communication, etc. Inaddition, the codebook proposed in the present disclosure may be usedfor a multi-antenna communication system using MIMO characteristics.Alternatively, the codebook may be used as a codebook formulti-layer/hierarchical layer transmission in broadcasting. Theabove-described embodiments of the present disclosure correspond tocombinations of the elements and features of the present disclosure. Theelements or features may be considered to be selective unless otherwisementioned. Each element or feature may be practiced without beingcombined with other elements or features. In addition, an embodiment ofthe present disclosure may be constructed by combining some of theelements and/or features. The sequences of operation in the embodimentsof the present disclosure may be changed. The configurations or featuresof an embodiment may be included in another embodiment or replaced withthe corresponding configurations or features of another embodiment. Itis obvious to those skilled in the art that claims that are notexplicitly cited in each other in the appended claims may be presentedin combination as an embodiment of the present disclosure or included asa new claim by a subsequent amendment after the application is filed.

It will be appreciated by those skilled in the art that the presentdisclosure can be carried out in other specific ways than those setforth herein without departing from the essential characteristics of thepresent disclosure. The above embodiments are therefore to be construedin all aspects as illustrative and not restrictive. The scope of thedisclosure should be determined by the appended claims and their legalequivalents, not by the above description, and all changes coming withinthe meaning and equivalency range of the appended claims are intended tobe embraced therein.

INDUSTRIAL APPLICABILITY

The method for performing MM-based NOMA communication and devicetherefor are industrially applicable to wireless communication systemssuch as the 3GPP LTE/LTE-A system, 5G system, etc.

1. A method of performing, by a user equipment (UE), multi-dimensionalmodulation (MM) based non-orthogonal multiple access (NOMA)communication, the method comprising: receiving, from a base station,control information indicating a UE-specific codebook for the UE in acodebook set predefined for an MM-based encoder; and receiving adownlink data channel from the base station based on the indicatedUE-specific codebook or transmitting an uplink data channel afterperforming MM-based encoding based on the indicated UE-specificcodebook.
 2. The method of claim 1, wherein the predefined codebook setis configured such that interference from multiple UEs caused bysuperposition access of the multiple UEs is minimized.
 3. The method ofclaim 1, wherein the predefined codebook set is configured such thatwhen the base station performs decoding, complexity of a message passingalgorithm (MPA) is minimized.
 4. The method of claim 1, wherein theindicated UE-specific codebook is configured such that a Euclideandistance between complex column vectors in the indicated UE-specificcodebook is maximized.
 5. The method of claim 1, wherein the controlinformation is received through a downlink control channel, radioresource control (RRC) signaling, or periodic control signaling.
 6. Themethod of claim 1, wherein the control information further includesinformation on a modulation and coding scheme (MCS) index.
 7. A methodof performing, by a base station, multi-dimensional modulation (MM)based non-orthogonal multiple access (NOMA) communication, the methodcomprising: selecting a user equipment (UE) specific codebook for a UEfrom a codebook set predefined for an MM-based encoder and performingMM-based encoding of channel-coded bits based on the selectedUE-specific codebook; and transmitting, to the UE, control informationincluding information indicating the selected UE-specific codebook,wherein the MM-based encoding is applied to the control information; andtransmitting, to the UE, a downlink data channel based on the indicatedUE-specific codebook or receiving, from the UE, an uplink data channelto which the MM-based encoding is applied based on the indicatedUE-specific codebook.
 8. A user equipment (UE) for performingmulti-dimensional modulation (MM) based non-orthogonal multiple access(NOMA) communication, the UE comprising: a receiver; a transmitter; anda processor, wherein the processor is configured to: control thereceiver to receive, from a base station, control information indicatinga UE-specific codebook for the UE in a codebook set predefined for anMM-based encoder; and control the receiver to receive a downlink datachannel from the base station based on the indicated UE-specificcodebook or control the transmitter to transmit an uplink data channelafter performing MM-based encoding based on the indicated UE-specificcodebook.
 9. The UE of claim 8, wherein the predefined codebook set isconfigured such that interference from multiple UEs caused bysuperposition access of the multiple UEs is minimized.
 10. The UE ofclaim 8, wherein the predefined codebook set is configured such thatwhen the base station performs decoding, complexity of a message passingalgorithm (MPA) is minimized.
 11. The UE of claim 8, wherein theindicated UE-specific codebook is configured such that a Euclideandistance between complex column vectors in the indicated UE-specificcodebook is maximized.
 12. The UE of claim 8, wherein the controlinformation is received through a downlink control channel, radioresource control (RRC) signaling, or periodic control signaling.
 13. TheUE of claim 8, wherein the control information further includesinformation on a modulation and coding scheme (MCS) index.
 14. A basestation for performing multi-dimensional modulation (MM) basednon-orthogonal multiple access (NOMA) communication, the base stationcomprising: a processor configured to: select a user equipment (UE)specific codebook for a UE from a codebook set predefined for anMM-based encoder, and perform MM-based encoding of channel-coded bitsbased on the selected UE-specific codebook; a transmitter configured totransmit, to the UE, control information including informationindicating the selected UE-specific codebook, wherein the MM-basedencoding is applied to the control information; and a receiverconfigured to: transmit, to the UE, a downlink data channel based on theindicated UE-specific codebook, or receive, from the UE, an uplink datachannel to which the MM-based encoding is applied based on the indicatedUE-specific codebook.